The Mathematical Principles of Natural Philosophy (1729)

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For other English-language translations of this work, see The Mathematical Principles of Natural Philosophy.
The Mathematical Principles of Natural Philosophy (1729)
by Isaac Newton, translated by Andrew Motte

An English translation by Andrew Motte, based on the 1726 3rd edition of Philosophiae Naturalis Principia Mathematica.

Title page

Front Matter
Title Page i
Dedication iii
The Author's Preface vii
The Preface of Mr Roger Cotes xiv
Definitions 1
Axioms, or Laws of Motion 19
Book 1: The Motion of Bodies
Section I 41
Section II 57
Section III 79
Section IV 94
Section V 104
Section VI 143
Section VII 154
Section VIII 168
Section IX 177
Section X 196
Section XI 218
Section XII 263
Section XIII 292
Section XIV 311
Book 2: The Motion of Bodies (in resisting mediums)
Section I 1
Section II 12
Section III 45
Section IV 55
Section V 64
Section VI 80
Section VII 111
Section VIII 163
Section IX 184
Book 3: Of the System of the World
Rules of Reasoning in Philosophy 202
Phænomena, or Appearances 206
Propositions I-IX (Force of gravity) 213
Propositions X-XXIV (Motions of the sea) 230
Propositions XXV-XXXIII (Motions of the moon) 262
Propositions XXXVI-XXXVIII (Forces to move the sea) 305
Lemmas I-III, Proposition XXXIX (Precession of equinoxes) 315
Lemmas IV-XI, Propositions XL-XLII (Comets) 323
General Scholium 387
Index XX
Appendix i
The Laws of the Moon's Motion according to Gravity (John Machin) (1)
Errata XX

Book 1[編集]

  1. Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow [1]
  2. Of the invention of centripetal forces [2]
  3. Of the motion of bodies in eccentric Conic sections [3]
  4. Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given [4]
  5. How the orbits are to be found when neither focus is given [5]
  6. How the motions are to be found in given orbits [6]
  7. Concerning the rectilinear ascent and descent of bodies [7]
  8. Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force [8]
  9. Of the motion of bodies in movable orbits; and of the motion of the apsides [9]
  10. Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies [10]
  11. Of the motions of bodies tending to each other with centripetal forces [11]
  12. Of the attractive forces of sphaerical bodies [12]
  13. Of the attractive forces of bodies which are not of a sphaerical figure [13]
  14. Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body [14]

Book 2[編集]

THE MOTION OF BODIES (In resisting mediums)
  1. Of the Motion of Bodies that are resisted in the ratio of the Velocity [15]
  2. Of the Motion of Bodies that are resisted in the duplicate ratio of their Velocities [16]
  3. Of the Motions of Bodies which are resisted partly in the ratio of the Velocities, and partly in the duplicate of the same ratio [17]
  4. Of the circular motion of bodies in resisting mediums [18]
  5. Of the density and compression of fluids; and of Hydrostatics [19]
  6. Of the motion and resistance of funependulous bodies [20]
  7. Of the motion of fluids and the resistance made to projected bodies [21]
  8. Of motion propagated thro' fluids [22]
  9. Of the circular motion of fluids [23]

Book 3[編集]

Motion of the satellites of Jupiter [28]
Propositions 2: the primary Planets, and 3: the Moon [29]
Proposition 6: Gravitation towards every Planet [30]
Proposition 7: Gravity tending to all Bodies [31]
Proposition 10: Longevity of planetary motions [32]
Proposition 11: Common centre of gravity of the Earth, the Sun and all the Planets [33]
Proposition 13: the Planets move in Ellipses [34]
Proposition 17: the diurnal motions of the Planets are uniform [35]
Proposition 18: (oblateness of the Planets & the Earth) [36]
Proposition 21: the equinoctial points go backwards [37]
Proposition 22: all the motions of the Moon ... follow from the principles ... laid down [38]
Proposition 24: the flux and reflux of the Sea, arise from the actions of the Sun and Moon [39]
Propositions 25-35: (disturbances of the motions of the Moon) [40]
Proposition 36-37: (forces of Sun & Moon to move the Sea) [41]
Proposition 38: Figure of the Moon's Body [42]
Proposition 39: precession of the equinoxes [43]
(Theory of the comets) [44]

References (not part of original work)[編集]

  1. Ducheyne, Steffen. "The General Scholium: Some notes on Newton’s published and unpublished endeavours, Lias: Sources and Documents Relating to the Early Modern History of Ideas, vol. 33, n° 2, pp. 223-274.". Retrieved 2008-11-19. 

 This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.


This work was published before January 1, 1928, and is in the public domain worldwide because the author died at least 100 years ago.


This work was published before January 1, 1928, and is in the public domain worldwide because the author died at least 100 years ago.